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In terms of the total post-tax savings value, I don't see how taxable (e.g. Roth) vs. tax-deferred (e.g. 401(k)) makes a difference.

Let me be specific. Suppose tax rate is s, and you dedicate X of pre-tax income per period to your savings for next T years. Suppose the account grows with an annual return rate r.

If you have a Roth account in which you put in post-tax income, you only contribute X * (1-r) per period, but you don't pay taxes later. In the end, the value of your total savings is sum_{t=1 to T} [X * (1-E) * (1+r)^(T-t)].

If you have a tax-deferred 401(k) account, you contribute X per period, but you pay taxes later. In the end, the value of your post-tax pension plan is {\sum_{t=1 to T} [X * (1+r)^(T-t)]} * (1-r).

These two are the same. Then, why does choosing tax-deferred make any difference?

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  • What exactly do you mean by taxable pension?
    – user102008
    Oct 20 at 20:38
  • @user102008 I should just say regular taxable savings. I'll edit the question. Thanks for the clarification.
    – J Li
    Oct 20 at 20:39
  • But in regular taxable savings, why would you "not pay taxes later"? You would owe taxes every year for earnings on that account.
    – user102008
    Oct 20 at 20:40
  • @user102008 Hmm, then I was wrong to say this applies to regular taxable savings. I'm thinking about things like a Roth account. Would that make more sense?
    – J Li
    Oct 20 at 20:42
  • Yes, it makes sense to compare Traditional and Roth (IRA/401k) accounts, but both of them are clearly more advantageous than a regular taxable account.
    – user102008
    Oct 20 at 20:44
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These two are the same. Then, why does choosing tax-deferred make any difference?

If the tax rates are different then, the two situations aren't equal.

If the rate will be lower in the future then put your money into pre-tax account.

If the rates will be higher in the future then put your money into an account that works like a Roth account. Pay the lower rates now, to never pay in the future.

Over your career you might transition your contributions from all Roth, to a mix, and finally to all traditional pre-tax account.

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  • That is very helpful. I somehow got the impression that "tax-deferred" is always better, but your explanation made it clear that this isn't the case. At a minimum, when someone is young and paying very low tax rates, they are better off putting money into taxable accounts... because their tax rates will go up in to the future. Tax-deferred isn't always better.
    – J Li
    Oct 20 at 20:33
  • In the United States I was talking about a Roth account. Pay tax today on the conyributions, and the withdrawals are tax free in retirement. All the growth and dividends are also tax free. Oct 20 at 21:02
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For simplicity, assume that the income tax rate is 20%. You initially have $1000 to invest, you can add to or remove from your investment at any time, and your investment will return 10% per year.

Paying taxes each year:

Initial investment:    $1000
First year income:      +200
Net before taxes:       1200
First year taxes:        -20 (10% of 1200-1000)
Net after first year:  $1180

Reinvesting the $180 gives for the second year
Investment amount:     $1180
Second year income:     +236
Net before taxes:       1416
Second year taxes:       -23.6 (10% of 1416-1180)
Net after second year: $1392.4

Now do the same thing with income taxes deferred until the end of the second year:

Initial investment:    $1000
First year income:      +200
Net after first year:  $1200

Reinvesting the $200 gives for the second year
Investment amount:     $1200
Second year income:     +240
Net before taxes:       1440
Taxes after second year: -44 (10% of 1440-1000)
Net after two years:   $1396

$1396 is, obviously, greater than $1392.4; you make more money when you postpone paying taxes. That's because you get to invest the money that you would have paid in taxes. And the longer you defer taxes the more you benefit from being able to invest that money.

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  • 1
    This isn't addressing the question that was asked, once it was clarified. Oct 21 at 18:06
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There are two classic reasons why the tax-deferred is preferable.

Growth inside the tax deferred account is also tax free.

At 5% growth over ten years with 20% tax, your $1000 is:

tax deferred: (1000 * (1 + 0.05)^10)*0.8 = $1303

tax paid = 1000*0.8 *(1 + (0.05*0.8) = $1184

You expect to be paying less tax in retirement.

Most people have a lower gross income in retirement, and so pay a lower proportion of that income in tax. It makes sense to shift the tax payment to later when the marginal tax rate is lower.

In many cases (for example the Canadian RRSP) you can also withdraw your retirement savings in an emergency. For example, if you lose your job or are sick you can withdraw from your retirement account, paying the appropriate atax. but again in those circumstances the tax burden is lower if you do not have a salary coming in.

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    Mapping to my original question, the key is that the marginal tax rate needs to be lower in retirement. That's the key assumption. Otherwise, if tax rates are the same, then tax-deferred doesn't carry any benefit, right?
    – J Li
    Oct 20 at 20:32
  • It is key to the second point that the marginal tax rate needs to be lower. The first does not require it. Oct 20 at 20:33
  • For taxable you mean 1000*0.8*(1+.05*.8)^10, but for Roth (assuming you reach 59.5 before distributing) it's 1000*0.8*(1+.05)^10 = 1302 Oct 22 at 2:27
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Another key observation, specific to the US Roth vs conventional IRA/401(k), is that the contribution limit on the Roth is effectively higher by your marginal tax rate. Indeed, you can contribute "$6000" to either type of IRA per year, or $7000 after age 50, but those $6000 in a conventional IRA are pre-tax, so if your marginal tax rate in retirement is 20% you've really only deposited $4800. In a Roth account, you pay the tax and then deposit $6000 which will never be taxes again. The same argument goes, with higher limits, for the 401(k), although those with high enough incomes to max out their 401(k) contributions are likely not to want to pay the high marginal rates to get pure Roth.

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